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Given a set V of n elements and a distance matrix [d ij ] n×n among elements, the max-mean dispersion problem (MaxMeanDP) consists in selecting a subset M from V such that the mean dispersion (or distance) among the selected elements is maximized. Being a useful model to formulate several relevant applications, MaxMeanDP is known to be NP-hard and thus computationally difficult. In this paper, we present a highly effective memetic algorithm for MaxMeanDP which relies on solution recombination and local optimization to find high quality solutions. Computational experiments on the set of 160 benchmark instances with up to 1000 elements commonly used in the literature show that the proposed algorithm improves or matches the published best known results for all instances in a short computing time, with only one exception, while achieving a high success rate of 100%. In particular, we improve 59 previous best results out of the 60 most challenging instances. Results on a set of 40 new large instances with 3000 and 5000 elements are also presented.The key ingredients of the proposed algorithm are investigated to shed light on how they affect the performance of the algorithm.

In this paper, an efficient heuristic algorithm for geometry optimization of bimetallic clusters is proposed. The algorithm is mainly composed of three ingredients: the monotonic basin-hopping method with guided perturbation (MBH-GP), surface optimization method, and iterated local search (ILS) method, where MBH-GP and surface optimization method are used to optimize the geometric structure of a cluster, and the ILS method is used to search the optimal homotop for a fixed geometric structure. The proposed method is applied to Cu(38-n)Au(n) (0 ≤ n ≤ 38), Ag(55-n)Au(n) (0 ≤ n ≤ 55), and Cu(55-n)Au(n) (0 ≤ n ≤ 55) clusters modeled by the many-body Gupta potential. Comparison with the results reported in the literature indicates that the present method is highly efficient and a number of new putative global minima missed in the previous papers are found. The present method should be a promising tool for the theoretical determination of ground-state structure of bimetallic clusters. Additionally, some key elements and properties of the present method are also analyzed.

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The NP-hard capacitated clustering problem (CCP) is a general model with a number of relevant applications. This paper proposes a highly effective iterated variable neighborhood search (IVNS) algorithm for solving the problem. IVNS combines an extended variable neighborhood descent method and a randomized shake procedure to explore effectively the search space. The computational results obtained on three sets of 133 benchmarks reveal that the proposed algorithm competes favorably with the state-of-the-art algorithms in the literature both in terms of solution quality and computational efficiency. In particular, IVNS discovers an improved best known result (new lower bounds) for 28 out of 83 most popular instances, while matching the current best known results for the remaining 55 instances. Several essential components of the proposed algorithm are investigated to understand their impacts on the performance of algorithm.

An equitable k-coloring of an undirected graph G = (V, E) is a partition of its vertices into k disjoint independent sets, such that the cardinalities of any two independent sets differ by at most one. As a variant of the graph coloring problem (GCP), the equitable coloring problem (ECP) concerns finding a minimum k for which an equitable k-coloring exists. In this work, we propose a backtracking based iterated tabu search (BITS) algorithm for solving the ECP approximately. BITS uses a backtracking scheme to define different k-ECP instances, an iterated tabu search approach to solve each particular k-ECP instance for a fixed k, and a binary search approach to find a suitable initial value of k. We assess the algorithm's performance on a set of commonly used benchmarks. Computational results show that BITS is very competitive in terms of solution quality and computing efficiency compared to the state-of-the-art algorithm in the literature. Specifically, BITS obtains new upper bounds for 21 benchmark instances, while matching the previous best upper bound for the remaining instances. Finally, to better understand the proposed algorithm, we study how its key ingredients impact its performance.

In this paper, a global optimization method is presented to determine the global-minimum structures of atomic clusters, where several already existing techniques are combined, such as the dynamic lattice searching method and two-phase local minimization method. The present method is applied to some selected large-sized Lennard-Jones (LJ) clusters and silver clusters described by the Gupta potential in the size range N = 13-140 and 300. Comparison with the results reported in the literature shows that the method is highly efficient and a lot of new global minima missed in previous papers are found for the silver clusters. The method may be a promising tool for the theoretical determination of ground-state structure of atomic clusters. Additionally, the stabilities of silver clusters are also analyzed and it is found that in the size range N = 13-140 there exist 12 particularly stable clusters.